Question

Consider the following investment opportunity: Initial cost $100,000, Additional cost at end of Year 1 150,000, Benefit at end of Year 1 0, Annual benefit per year at end of Years 2-10 20,000, With interest at 5%, what is the benefit-cost ratio for this project?

Answer 1

The benefit-cost ratio for this project is approximately 0.409.

Step-by-step explanation:

The benefit-cost ratio for this project can be calculated by dividing the present value of all benefits by the present value of all costs.

Let's calculate the present value of costs first:

• Year 0: $100,000
• Year 1: $150,000
• Years 2-10: $20,000 per year

Using a discount rate of 5%, we can calculate the present value of costs as follows:

Calculate the present value of Year 1 cost:

$150,000 / (1+0.05)

= $142,857

Calculate the present value of Years 2-10 costs:

$20,000 / (1+0.05)^2 + $20,000 / (1+0.05)^3 + ... + $20,000 / (1+0.05)^10

= $167,754

Add the present values of all costs:

$100,000 + $142,857 + $167,754

= $410,611

Next, let's calculate the present value of benefits:

Years 2-10: $20,000 per year

Using the same discount rate of 5%, we can calculate the present value of benefits as follows:

Calculate the present value of Years 2-10 benefits:

$20,000 / (1+0.05)^2 + $20,000 / (1+0.05)^3 + ... + $20,000 / (1+0.05)^10

= $167,754

Add the present values of all benefits: $167,754

Finally, calculate the benefit-cost ratio by dividing the present value of benefits by the present value of costs:

Benefit-Cost Ratio = $167,754 / $410,611

≈ 0.409